An investigation of errors in estimates of the cometary nuclei active area fractions

Active area fractions of cometary nuclei are often estimated by comparing the observed water production rates with theoretical rates obtained by applying the fast rotator or subsolar point approximations to spherical model nuclei. Any discrepancy between observed and theoretical production rates is interpreted as a certain degree of dust mantling (or in some cases hyper activity) of the object. We here investigate the typical errors introduced in such active area fraction estimates by the usage of oversimplified spherical model nuclei. This is done by first calculating the production rates of slowly rotating irregular model bodies with different activity patterns on their surfaces and arbitrary spin axis orientations, for which solar illumination is treated properly. Next, the production rates of the spherical model objects under averaged insolation are compared to the production rates of the complex model objects in an attempt to recover the known active area fraction of the latter bodies. We then find that the fast rotator and subsolar point approximations generally yield large over- and underestimates of the active area fraction, depending on the characteristics of the simulated complex nuclei. Acceptable relative errors (<100%) only occur at small heliocentric distances, and the subsolar point approximation yields somewhat better results than the fast rotator approximation.